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arXiv 1506.04538gr-qchep-th
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标量不变量为零的电磁场

Electromagnetic fields with vanishing scalar invariants

Marcello Ortaggio, Vojtěch Pravda

摘要:

我们确定了在$n$维时空中任意阶具有消失标量不变量(VSI)的$p$ -形式$F$的类.也就是说,我们证明了$F$是VSI当且仅当它是N型的,它的多重零方向$l$是“退化的Kundt”,以及$\nabla_{l}F=0$。结果是理论独立的。接下来,我们讨论麦克斯韦场的特殊情况,在测试场和完整的爱因斯坦-麦克斯韦方程组的水平。这些描述了电磁非膨胀波在不同的孔特时空中传播。我们进一步指出,这些解决方案的一个子集拥有一个普遍的性质,即,他们还解决(实际上)任何广义(非线性和更高的导数)电动力学,也可能耦合到爱因斯坦的引力。

英文摘要:

We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is "degenerate Kundt", and $\nabla_{l}F=0$. The result is theory-independent. Next, we discuss the special case of Maxwell fields, both at the level of test fields and of the full Einstein-Maxwell equations. These describe electromagnetic non-expanding waves propagating in various Kundt spacetimes. We further point out that a subset of these solutions possesses a universal property, i.e., they also solve (virtually) any generalized (non-linear and with higher derivatives) electrodynamics, possibly also coupled to Einstein's gravity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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